| Abstract:
The problem of describing the injective envelope of a simple
left module over a left noetherian ring has been studied
extensively, with a dominant role being played by the prime ideals
of the ring, and uniform modules over such rings have been
classified into either tame or wild.
In
the case of the skew Laurent polynomial ring B the only prime ideal
is 0, and the only tame module is the ring itself, the injective
envelope of this tame module being the quotient field of the ring.
It seems that it is not an easy task to study the (indecomposable)
injective envelopes of a simple non-zero left B-module. The study
of the elementary socle series of the envelope will give us some
description, which will lead to a localization of the ring.
Hopefully, this new direction will shade some light into the
structure of these peculiar uniform wild B-modules.
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